Cells are like eggs. They come in fixed voltages and capacities. You can't get half an egg, and you can't get half a cell, at least in voltage. A NiCad or NiMH cells are 1.2 volts nominal, lead acid is 2.0 volts nominal and the various lithium technologies are about 3.6 volts per cell. If you need more voltage you have to add them in series, if you need less voltage you need some kind of voltage regulator or DC/DC converter.

If you need more current you may need to put cells in parallel. If you need more capacity you may also put cells in parallel.

Many times the physical configuration makes it more attractive to use many small cells rather than a few large cells.

Is there a way to charge my iPhone while it is turned off?

You may have tried to charge your iPhone while it was powered off only to have it turn itself on as soon as you plug it in to the USB cable or place it on the dock. As a result, it may have seemed that the iPhone insists on being turned on in order to charge.

As it turns out, this is not the case. Simply plug your iPhone in to charge while turned on (or off for that matter) and once it begins charging, power it down. If you power down after charging begins, the iPhone will remain turned off while still charging.

What is the typical material used to separate the anode and cathode in Li-ion batteries?

The anode and cathode have a liquid electrolyte between them that conducts the Li-ion. There is a polymer separator that electrically isolates the anode and cathode; it is a thin membrane of porous polypropylene or polyethylene film.